INTRODUCTION Solving quantum many-body problems, such as finding ground states of quantum systems, has far-reaching consequences for physics, materials science, and chemistry. Classical computers have facilitated many profound advances in science and technology, but they often struggle to solve such problems. Scalable, fault-tolerant quantum computers will be able to solve a broad array of quantum problems but are unlikely to be available for years to come. Meanwhile, how can we best exploit our powerful classical computers to advance our understanding of complex quantum systems? Recently, classical machine learning (ML) techniques have been adapted to investigate problems in quantum many-body physics. So far, these approaches are mostly heuristic, reflecting the general paucity of rigorous theory in ML. Although they have been shown to be effective in some intermediate-size experiments, these methods are generally not backed by convincing theoretical arguments to ensure good performance. RATIONALE A central question is whether classical ML algorithms can provably outperform non-ML algorithms in challenging quantum many-body problems. We provide a concrete answer by devising and analyzing classical ML algorithms for predicting the properties of ground states of quantum systems. We prove that these ML algorithms can efficiently and accurately predict ground-state properties of gapped local Hamiltonians, after learning from data obtained by measuring other ground states in the same quantum phase of matter. Furthermore, under a widely accepted complexity-theoretic conjecture, we prove that no efficient classical algorithm that does not learn from data can achieve the same prediction guarantee. By generalizing from experimental data, ML algorithms can solve quantum many-body problems that could not be solved efficiently without access to experimental data. RESULTS We consider a family of gapped local quantum Hamiltonians, where the Hamiltonian H ( x ) depends smoothly on m parameters (denoted by x ). The ML algorithm learns from a set of training data consisting of sampled values of x , each accompanied by a classical representation of the ground state of H ( x ). These training data could be obtained from either classical simulations or quantum experiments. During the prediction phase, the ML algorithm predicts a classical representation of ground states for Hamiltonians different from those in the training data; ground-state properties can then be estimated using the predicted classical representation. Specifically, our classical ML algorithm predicts expectation values of products of local observables in the ground state, with a small error when averaged over the value of x . The run time of the algorithm and the amount of training data required both scale polynomially in m and linearly in the size of the quantum system. Our proof of this result builds on recent developments in quantum information theory, computational learning theory, and condensed matter theory. Furthermore, under the widely accepted conjecture that nondeterministic polynomial-time (NP)–complete problems cannot be solved in randomized polynomial time, we prove that no polynomial-time classical algorithm that does not learn from data can match the prediction performance achieved by the ML algorithm. In a related contribution using similar proof techniques, we show that classical ML algorithms can efficiently learn how to classify quantum phases of matter. In this scenario, the training data consist of classical representations of quantum states, where each state carries a label indicating whether it belongs to phase A or phase B . The ML algorithm then predicts the phase label for quantum states that were not encountered during training. The classical ML algorithm not only classifies phases accurately, but also constructs an explicit classifying function. Numerical experiments verify that our proposed ML algorithms work well in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases. CONCLUSION We have rigorously established that classical ML algorithms, informed by data collected in physical experiments, can effectively address some quantum many-body problems. These rigorous results boost our hopes that classical ML trained on experimental data can solve practical problems in chemistry and materials science that would be too hard to solve using classical processing alone. Our arguments build on the concept of a succinct classical representation of quantum states derived from randomized Pauli measurements. Although some quantum devices lack the local control needed to perform such measurements, we expect that other classical representations could be exploited by classical ML with similarly powerful results. How can we make use of accessible measurement data to predict properties reliably? Answering such questions will expand the reach of near-term quantum platforms. Classical algorithms for quantum many-body problems. Classical ML algorithms learn from training data, obtained from either classical simulations or quantum experiments. Then, the ML algorithm produces a classical representation for the ground state of a physical system that was not encountered during training. Classical algorithms that do not learn from data may require substantially longer computation time to achieve the same task.
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IMG-DNA: Approximate DNA Storage for Images
Deoxyribonucleic Acid (DNA) as a storage medium with high density and long-term preservation properties can satisfy the requirement of archival storage for rapidly increased digital volume. The read and write processes of DNA storage are error-prone. Images
widely used in social media have the properties of fault tolerance which are well fitted to the DNA storage. However, prior work simply investigated the feasibility of DNA storage storing different types of data and simply store images in DNA storage, which did not fully investigate the fault-tolerant potential of images in the DNA storage. In this paper, we proposed a new image-based DNA system called IMG-DNA, which can efficiently store images in DNA
storage with improved DNA storage robustness. First, a new DNA architecture is proposed to fit JPEG-based images and improve the image’s robustness in DNA storage. Moreover, barriers inserted in DNA sequences efficiently prevent error propagation in images of DNA storage. The experimental results indicate that the proposed IMG-DNA achieves much higher fault-tolerant than prior work.
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- Award ID(s):
- 1812537
- NSF-PAR ID:
- 10276611
- Date Published:
- Journal Name:
- International Systems and Storage Conference (SYSTOR’21)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Motivation DNA-based data storage is a quickly growing field that hopes to harness the massive theoretical information density of DNA molecules to produce a competitive next-generation storage medium suitable for archival data. In recent years, many DNA-based storage system designs have been proposed. Given that no common infrastructure exists for simulating these storage systems, comparing many different designs along with many different error models is increasingly difficult. To address this challenge, we introduce FrameD, a simulation infrastructure for DNA storage systems that leverages the underlying modularity of DNA storage system designs to provide a framework to express different designs while being able to reuse common components.
Results We demonstrate the utility of FrameD and the need for a common simulation platform using a case study. Our case study compares designs that utilize strand copies differently, some that align strand copies using multiple sequence alignment algorithms and others that do not. We found that the choice to include multiple sequence alignment in the pipeline is dependent on the error rate and the type of errors being injected and is not always beneficial. In addition to supporting a wide range of designs, FrameD provides the user with transparent parallelism to deal with a large number of reads from sequencing and the need for many fault injection iterations. We believe that FrameD fills a void in the tools publicly available to the DNA storage community by providing a modular and extensible framework with support for massive parallelism. As a result, it will help accelerate the design process of future DNA-based storage systems.
Availability and implementation The source code for FrameD along with the data generated during the demonstration of FrameD is available in a public Github repository at https://github.com/dna-storage/framed, (https://dx.doi.org/10.5281/zenodo.7757762).
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null (Ed.)Fault-tolerant virtual machine (VM) placement refers to the process of placing multiple copies of the same VM cloud application inside cloud data centers. The challenge is how to place required number of VM replicas while minimizing the number of physical machines (PMs) that store them, in order to save energy consumption of cloud data centers. We refer to it as fault-tolerant VM placement problem. In our previous work, we have proposed a greedy algorithm to solve this problem. In this paper, we compare it with an existing research that is based on well-known Welsh Powell Graph-Coloring Algorithm to place items into bins while considering the conflicts between items and items and items and bins. Via extensive simulations, we show that our greedy algorithm can turn off 40-50% more PMs than existing work and can place upto four times as many VM replicas as existing work, achieving much stronger fault-tolerance with less energy consumption. We also compare both algorithms with the optimal integer lin- ear programming (ILP)-based algorithm, which serves as the benchmark of the comparison.more » « less
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Wang, H. (Ed.)Once upon a time databases were structured, one size fitted all and they resided on machines that were trustworthy and even when they failed, they simply crashed. This era has come and gone as eloquently stated by Stonebraker and Cetintemel [16]. We now have key-value stores, graph databases, text databases, and a myriad of unstructured data repositories. The database community has wholeheartedly accepted the fact that the same information might come in different formats, modes and representations. We also accept that data might not be ”clean” and that data might need to be ”cleaned” due to the diverse sources of information. However, we, as a database community still cling to our 20th century belief that databases always reside on trustworthy, honest servers. Although the database community has always considered fault-tolerance as an integral building block of data management (remember ”D” in ACID is for Durability), we still have trouble accepting the fact that not all failures are simply crash failures and might in fact involve malicious and non-trustworthy infrastructure. This notion has been challenged and abandoned by many other Computer Science communities, most notably the security and the distributed systems communities. The rise of the cloud computing paradigm as well as the rapid popularity of blockchains demand a rethinking of our na¨ıve, comfortable beliefs in an ideal benign infrastructure. In the cloud, clients store their sensitive data in remote servers owned and operated by cloud providers. The Security and Crypto Communities have made significant inroads to protect both data and access privacy from malicious untrusted storage providers using encryption and oblivious data stores. The Distributed Systems and the Systems Communities have developed consensus protocols to ensure the fault-tolerant maintenance of data residing on untrusted, malicious infrastructure. However, these solutions face significant scalability and performance challenges when incorporated in large scale data repositories. Novel database designs need to directly address the natural tension between performance, fault-tolerance and trustworthiness. This is a perfect setting for the database community to lead and guide.more » « less
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null (Ed.)A graph G is called {\em self-ordered} (a.k.a asymmetric) if the identity permutation is its only automorphism. Equivalently, there is a unique isomorphism from G to any graph that is isomorphic to G. We say that G=(VE) is {\em robustly self-ordered}if the size of the symmetric difference between E and the edge-set of the graph obtained by permuting V using any permutation :VV is proportional to the number of non-fixed-points of . In this work, we initiate the study of the structure, construction and utility of robustly self-ordered graphs. We show that robustly self-ordered bounded-degree graphs exist (in abundance), and that they can be constructed efficiently, in a strong sense. Specifically, given the index of a vertex in such a graph, it is possible to find all its neighbors in polynomial-time (i.e., in time that is poly-logarithmic in the size of the graph). We provide two very different constructions, in tools and structure. The first, a direct construction, is based on proving a sufficient condition for robust self-ordering, which requires that an auxiliary graph, on {\em pairs} of vertices of the original graph, is expanding. In this case the original graph is (not only robustly self-ordered but) also expanding. The second construction proceeds in three steps: It boosts the mere existence of robustly self-ordered graphs, which provides explicit graphs of sublogarithmic size, to an efficient construction of polynomial-size graphs, and then, repeating it again, to exponential-size(robustly self-ordered) graphs that are locally constructible. This construction can yield robustly self-ordered graphs that are either expanders or highly disconnected, having logarithmic size connected components. We also consider graphs of unbounded degree, seeking correspondingly unbounded robustness parameters. We again demonstrate that such graphs (of linear degree)exist (in abundance), and that they can be constructed efficiently, in a strong sense. This turns out to require very different tools. Specifically, we show that the construction of such graphs reduces to the construction of non-malleable two-source extractors with very weak parameters but with some additional natural features. We actually show two reductions, one simpler than the other but yielding a less efficient construction when combined with the known constructions of extractors. We demonstrate that robustly self-ordered bounded-degree graphs are useful towards obtaining lower bounds on the query complexity of testing graph properties both in the bounded-degree and the dense graph models. Indeed, their robustness offers efficient, local and distance preserving reductions from testing problems on ordered structures (like sequences) to the unordered (effectively unlabeled) graphs. One of the results that we obtain, via such a reduction, is a subexponential separation between the query complexities of testing and tolerant testing of graph properties in the bounded-degree graph model. Changes to previous version: We retract the claims made in our initial posting regarding the construction of non-malleable two-source extractors (which are quasi-orthogonal) as well as the claims about the construction of relocation-detecting codes (see Theorems 1.5 and 1.6 in the original version). The source of trouble is a fundamental flaw in the proof of Lemma 9.7 (in the original version), which may as well be wrong. Hence, the original Section 9 was omitted, except that the original Section 9.3 was retained as a new Section 8.3. The original Section 8 appears as Section 8.0 and 8.1, and Section 8.2 is new.more » « less
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